[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-125864-en":3,"doc-seo-125864-105":31,"detail-sidebar-cat-0-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},125864,1099523882367,"Hazel","https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc",8,"Research & Report","α-divergence improves the entropy production estimation via machine learning","Recent work focuses on estimating stochastic entropy production (EP) from trajectory data using machine learning, where performance depends on choosing a loss function that preserves accurate EP estimation. This study shows that variational representations of the α-divergence yield many valid loss functions for EP estimation. Fixing α within −1 to 0 improves robustness of α-NEEP under strong nonequilibrium driving and slow dynamics. The choice α = −0.5 delivers near-optimal results, supported by an exactly solvable simplification analyzing the loss landscape and stochastic properties.","arXiv :2303 .02901v2 [ cond-mat .stat-mech] 19 Jan 2024  \nα-divergence improves the entropy production estimation via machine learning  \nEuijoon Kwon 1 and Yongjoo Baek 1, ∗  \n1 Department of Physics and Astronomy & Center for Theoretical Physics,  \nSeoul National University, Seoul 08826, Republic of Korea  \n(Dated: January 22, 2024)  \nRecent years have seen a surge of interest in the algorithmic estimation of stochastic entropy production (EP) from trajectory data via machine learning. A crucial element of such algorithms is the identification of a loss function whose minimization guarantees the accurate EP estimation. In this study, we show that there exists a host of loss functions, namely those implementing a variational representation of the α-divergence, which can be used for the EP estimation. By fixing α to a value between −1 and 0, the α-NEEP (Neural Estimator for Entropy Production) exhibits a much more robust performance against strong nonequilibrium driving or slow dynamics, which adversely affects the existing method based on the Kullback-Leibler divergence (α = 0) . In particular, the choice of α = −0 .5 tends to yield the optimal results. To corroborate our findings, we present an exactly solvable simplification of the EP estimation problem, whose loss function landscape and stochastic properties give deeper intuition into the robustness of the α-NEEP.  \nI. INTRODUCTION  \nHow irreversible does a process look? One may pose this question for two distinct reasons. First, whether a biological process requires energy dissipation is often a subject of much debate [1, 2] . To resolve this issue, it is useful to note that irreversibility suggests energy dissipation. Various hallmarks of irreversibility, such as the breaking of the fluctuation-dissipation theorem [3] and the presence of nonequilibrium probability currents in the phase space [4, 5], have been used to determine whether energy is dissipated. Second, whether a nonequilibrium system allows for an effective equilibrium description isan important issue. For instance, in active matter, despite the energy dissipation at the microscopic level, it has been argued that the large-scale phenomena allow for an effective equilibrium description [6–10] . If we can quantify the irreversibility of an empirical process at various levels of coarse-graining [11, 12], it will provide us with helpful clues as to whether we should look for an effective equilibrium theory for the process.  \nBased on the framework of stochastic thermodynamics, modern thermodynamics assigns entropy production (EP) to each stochastic trajectory based on its irreversibility [13] . Thus, empirically measuring the irreversibility of a process is closely tied to the problem of estimating EP from sampled trajectories [14–21] . A straightforward approach to the problem is to evaluate the relevant transition probabilities by directly counting the number of trajectory segments, which is called the plug-in method [14, 15] . The method, readily applicable to discrete systems, can also be applied to continuous systems through the use of kernel functions [16] . However, while this method is simple and intuitive, it requires a huge ensemble of lengthy trajectories for accurate estimations (curse of dimensionality) . More re-  \n∗ [y.baek@snu.ac.kr](y.baek@snu.ac.kr)  \ncent studies proposed methods based on universal lower bounds of the average EP, such as the thermodynamic uncertainty relations [16–19] and the entropic bound [20] . While these methods do not suffer from the curse of dimensionality and are applicable even to non-stationary processes [19, 20], their accuracy is impaired when the underlying bounds are not tight. Moreover, these methods are applicable only to the estimation of the average EP, not the EP of each trajectory.  \nMeanwhile, with the advent of machine learning techniques in physics, a novel method for EP estimation using artificial neural networks has been developed [21] . This method, cal","cbCaidtHcZMPrdQe","https://ap.wps.com/l/cbCaidtHcZMPrdQe","pdf",3084576,3,1,11,"English","en",105,"# Introduction\n## Stochastic thermodynamics and EP estimation from trajectories\n## Existing methods: plug-in, uncertainty bounds, and NEEP\n# Overview of the original NEEP\n## Loss based on variational representation of KL divergence\n# α-NEEP and robustness\n## α-divergence variational loss functions\n## Optimality near α = −0.5","[{\"question\":\"What problem does this paper address in machine-learning EP estimation?\",\"answer\":\"It addresses the need for a loss function in which minimization guarantees accurate estimation of entropy production from trajectory data.\"},{\"question\":\"How does α-NEEP improve over the original NEEP?\",\"answer\":\"α-NEEP replaces the KL-based objective with a variational representation of the α-divergence, yielding more robust performance under strong nonequilibrium driving and poor phase-space sampling.\"},{\"question\":\"Why does α = −0.5 matter in the proposed framework?\",\"answer\":\"The study finds α = −0.5 tends to produce the optimal overall results and confirms this through an analytically tractable simplified model.\"}]","α-divergence improves the entropy production estimation via machine learning | 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problem does this paper address in machine-learning EP estimation?","Question",{"text":76,"@type":77},"It addresses the need for a loss function in which minimization guarantees accurate estimation of entropy production from trajectory data.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How does α-NEEP improve over the original NEEP?",{"text":81,"@type":77},"α-NEEP replaces the KL-based objective with a variational representation of the α-divergence, yielding more robust performance under strong nonequilibrium driving and poor phase-space sampling.",{"name":83,"@type":74,"acceptedAnswer":84},"Why does α = −0.5 matter in the proposed framework?",{"text":85,"@type":77},"The study finds α = −0.5 tends to produce the optimal overall results and confirms this through an analytically tractable simplified 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